This workshop is supported by KAKENHI grant number 24K00273.
Program
* Each speaker has 45 minutes including Q&A.
14:10-14:15: Opening
Session 1 (Chair: Shogo Kato)
"Index mixed copulas"
Marius Hofert (Hong Kong University)
Abstract:
The class of index-mixed copulas is introduced and its properties are investigated. Index-mixed copulas are constructed from given base copulas and a random index vector, and show a rather remarkable degree of analytical tractability. The analytical form of the copula and, if it exists, its density are derived. As the construction is based on a stochastic representation, sampling algorithms can be given. A particularly interesting feature of index-mixed copulas is that they allow one to provide a revealing interpretation of the well-known family of Eyraud-Farlie-Gumbel-Morgenstern (EFGM) copulas. Through the lens of index-mixing, one can explain why EFGM copulas can only model a limited range of concordance and are tail independent, for example. Index-mixed copulas do not suffer from such restrictions while remaining analytically tractable.
"Frank copula and relative local dependence"
Issey Sukeda (Tokyo University)
Abstract：
We demonstrate that the Frank copula is the minimum information copula under fixed Kendall’s τ, both theoretically and numerically. Our result asserts that selecting the Frank copula as an appropriate copula model is equivalent to using Kendall’s τ as the sole available information about the true distribution, based on the entropy maximization principle. In relation to this, we further modify the well-known notion of the local dependence and argue its properties.
15:45-16:00: Break
16:00- 17:30: Session 2 (Chair: Toshinao Yoshiba)
"Parametric inference for the Mann-Whitney effect under survival copulamodels"
Takeshi Emura (Hiroshima University)
Abstract:
Abstract: The Mann-Whitney effect is one of the most important measures for comparing the survival times of two independent groups. Under the independence assumption of two survival times, the Mann-Whitney effect can be estimated by Efron’s classical estimator. However, without the independence assumption, the Mann-Whitney effect cannot be estimated by the classical estimator without further assumptions. In this study, we use parametric copulas to model the joint distribution of two survival times, and propose an inference procedure for the Mann-Whitney effect under dependence models. We also derive the asymptotic variance estimator of the Mann-Whitney effect under various copulas and parametric marginal distributions, and conduct simulation studies to evaluate the accuracy of the proposed estimators. Finally, the proposed inference procedures are illustrated using a real dataset.
"Robust risk evaluation of joint life insurance under dependence uncertainty"
Takaaki Koike (Hitotsubashi University)
Abstract:
Dependence among multiple lifetimes plays important roles in pricing joint life insurance products. When available data and information are limited, the dependence structure is exposed to model uncertainty. We address robust pricing and risk evaluation of joint life insurance products against dependence uncertainty among lifetimes. For various insurance products and dependence uncertainty structures, we present analytical formulas and computational methods for calculating the most conservative and anti-conservative price and risk evaluations.